Time-consistent investment and reinsurance strategies under thinning-dependence structure

Accepted by: Dr. Giorgio ConsigliThis study investigates an optimal investment and reinsurance problem for a general insurance company that owns shares of an insurer and a reinsurer using a mean-variance framework. To depict the characteristics of dependence between insurance businesses of the insurer and reinsurer, the claim processes are governed by a compound Poisson risk model with a thinning-dependence structure. Both the insurer and the reinsurer are permitted to invest in a common risk-free asset and different risky assets to increase their respective wealth, where the two risky assets are correlated. By solving the extended Hamilton-Jacobi-Bellman equation within the game theoretic framework, we derive explicit expressions of the optimal time-consistent strategies and the value function. Our findings reveal that thinning parameters play a crucial role in shaping the decision-making processes of the insurer and the reinsurer, enabling them to effectively hedge and mitigate risks. To further illustrate the impacts of model parameters on optimal strategies and provide economic insights, we conduct sensitivity analyses and present some numerical examples.